Sustained dynamic transience in a Lotka-Volterra competition model system for grassland species

Theoretical approaches, such as the Lotka-Volterra framework, enable predictions about long term species coexistence based on stability criteria, but generally assume temporal constancy of system equations and parameters. In real world systems, temporal variability may interfere with the attainment of stable states. Managed grassland ecosystems in Northwestern Europe experience structural periodic fluctuations in environmental conditions: the seasons. In addition, periodic disturbances such as cutting are very common. Here we show, using a Lotka-Volterra system applied to grassland species with empirically derived parameters, that seasonal variability can result in a time dependent equilibrium and redirection of displacement processes.Parameter estimates differed between species and - in most cases - between the seasons. As a result, five of the fifteen tested species combinations had different outcomes of species interactions between seasons. This indicates that systems remain in dynamic transience over the year as the equilibrium changes and the species composition of the system follows the equilibrium without ever attaining it. The non-attainment of the steady state enables coexistence of species even if there is competitive exclusion in one of the seasons. For three of the fifteen species combinations, cutting frequency affected the long-term coexistence patterns. Cutting resets the biomass of competing species and favours during regrowth those species that have a high growth rate, which can alter species coexistence in comparison to a Lotka-Volterra model without cutting. The Lotka-Volterra framework with seasonally changing empirical parameters predicts coexistence as a possible outcome of systems that in component seasons are characterised by exclusion, and vice versa.     

Feasibility and stability in randomly assembled Lotka-Volterra models

For a Lotka-Volterra model to represent a viable ecosystem it's nontrivial equilibrium must be feasible. If m is the number of species, it is shown that in a set of randomly assembled Lotka-Volterra models, the fraction of models with a feasible equilibrium is some function of m which behaves like 2^?m. Moreover a subset of Lotka-Volterra models, each of which has a feasible equilibrium, has the same stability property as a set of linear models which is assembled randomly in the same manner. This contradicts a recent claim that a Lotka-Volterra model with a feasible equilibrium tends to be stable. Thus for two reasons the probability that a Lotka-Volterra model represents a viable and stable ecosystem decreases rapidly with the number of species. This supports the theme developed by May that stability in model ecosystems decreases with diversity.     

Morphological analysis of growth forms of branching marine sessile organisms along environmental gradients

In this paper a series of growth forms of the sponge Haliclona oculata, the hydrozoan Millepora alcicornis and the scleractinian coral Pocillopora damicornis are morphologically analysed. The growth forms of these species were collected along a gradient of the amount of water movement. In this analysis it is demonstrated that, although these species are from very different taxonomical groups, the degree of compactness of the growth forms shows a similar trend as a response to the exposure to water movement. In all three species the growth forms gradually change from thin-branching to more compact shapes, as evaluated by measurements of various morphological characteristics. Other morphological measurements, in particular the average distance between branch tips and neighbouring branches (“branch spacing”) show a more species-specific pattern. Species in which fusion of branches is almost never observed, as for example P. damicornis, are characterized by a relatively low standard deviation of branch spacing. Species in which anastomosis frequently occurs (H. oculata and M. alcicornis) are characterized by a relatively high standard deviation in branch spacing. The final aim of this research approach is to use the morphological data acquired here in combination with morphological simulation models to gain a better understanding of the growth and form of these organisms and the impact of the physical environment (hydrodynamics and availability of light required for photosynthesis). Received: 8 July 1998 / Accepted: 9 February 1999     

Analysing sperm competition data: simple models for predicting mechanisms

Summary Prospective models are developed for analysing sperm competition data so as to predict the underlying mechanisms determining paternity in multiply mated females. The models require: 1) estimations of proportion of offspring sired by the last male to mate (P ₂), 2) knowledge of the number of sperm transferred by each male, and 3) knowledge of the sperm storage capacity of the female, should this be limited. They will distinguish between raffles (sperm mixing without displacement) and sperm displacement mechanisms. The sensitivity of the techniques can be increased by manipulating the number of sperm transferred by each male. Typically, this can be done by manipulating copula duration or number of ejaculations, given a knowledge of the rate of sperm transfer. Data from two contrasting insect species are fitted to the models to demonstrate the techniques. These models are prospective only, and their limitations are discussed. The principal limitation is that we assume that sperm used for fertilization mix randomly in a fertilization set immediately prior to fertilization; in reality this may be difficult to identify. When sperm mixing is very rapid, the fertilization set will often be equivalent to the sperm stores, but with slow mixing, the fertilization set may be equivalent to a much more restricted zone and may change with time. Offprint requests to: G.A. Parker     

Analysis of competition models in periodic medium

We propose special models (the so-called D-systems) with periodic delta-functions being used as the growth velocities of the populations. This allows to build, in a practically explicit form, corresponding Poincare mapping and to reveal a series of “paradoxical” phenomena and selection criteria in the dynamics of the competitors. For the analysis of non-autonomous models, new general principle of inheritance of a series of local properties by the global Poincare shift mapping is worked up. Specifically, key heritable properties are determined for non-autonomous competition models. The selection criterion for competitive selection, based on the concept of the universal allowance constant, is derived in this work.     

Competitive interactions among sessile organisms in Tomioka Bay,south Japan: importance of light conditions on the panel surface

Interspecific competitive interactions among sessile epibenthos were studied by suspending PVC panels at Tomioka Bay, south Japan, for a maximum period of 16 mo. Interactions were monitored from photographs of a fixed area of the panels. Four panels were suspended during two different months in autumn 1991, and the development of the community was followed until December 1992. Altogether, 6511 interspecific overgrowth interactions were recorded, of which 37 resulted in standoffs and the rest in overgrowths. The competitive relationship observed in this sessile assemblage followed the pattern of a hierarchy with numerous backloops. Among the 36 species, belonging to the seven taxonomic groups encountered during the study, the colonial ascidian Didemnum moseleyi was recorded as the dominant species (with respect to competitive ability) while the barnacle Balanus trigonus was the weakest species. The month of panel exposure and whether or not the panel surface was shaded had a significant influence on the competitive ability of the sessile organisms. The order of hierarchy of the most dominant species changed with the month of panel submersion and its light conditions. Among the several abundant species tested, longer residence times were recorded for serpulid worms than for the colonial species. A significant, positive relationship was obtained between the areal cover of competitively dominant sessile organisms and the number of their interspecific interactions. From the short residence time of sessile organisms and the significant relationship between their areal cover and number of interspecific interactions, it is concluded that the interspecific interactions played important role in the species succession.     

Mechanisms of sperm competition in birds: mathematical models

Summary We built models of sperm competition and compared their predictions with observations from domestic chickens in an attempt to elucidate the mechanism of sperm competition. The models suggest that (1) observed levels of precedence of sperm are not merely a passive consequence of the greater mortality of sperm from earlier inseminations; (2) displacement of existing sperm from sperm storage tubules by incoming sperm explains observed levels of sperm precedence and disappearance from the reproductive tract, even in the absence of recognition of sperm from different inseminations; (3) stratification of sperm within the sperm storage tubules fails as an explanation of observed patterns of sperm precedence and disappearance because long-term levels of sperm precedence as high as those observed can only be predicted in combination with rates of disappearance of sperm much lower than those observed in chickens. The predictions of sperm precedence levels following multiple inseminations also suggest that displacement rather than stratification is the most likely mechanism of sperm competition in chickens. We discuss the consequences of male or female control of sperm competition, non-uniform distribution of sperm between sperm storage tubules, and variation in sperm precedence with time after the last insemination, and suggest ways in which the models may be used in future to aid in the elucidation of mechanisms of sperm competition. Offprint requests to: C.M. Lessells     

New hydroepidemiological models of indicator organisms and zoonotic pathogens in agricultural watersheds

Simple analytical models are derived to assess how a series of cattle animal farms affect the transport and fate of an indicator organism (Escherichia coli) and a zoonotic pathogen (Campylobacter) in a stream. Separate steady-state mass-balance models are developed and solved for the ultimate minimum and maximum concentrations for the two organisms. The E. coli model assumes that the organism is ubiquitous and abundant in the animals’ digestive tracts. In contrast, a simple dose-response model is employed to relate the Campylobacter prevalence to drinking water drawn from the stream. Because faecal indicators are commonly employed to assess the efficacy of best management practice (BMP) interventions, we also employ the models to assess how BMPs impact pathogen levels. The model provides predictions of (a) the relative removal efficacy for Campylobacter and (b) the prevalence of Campylobacter infection among farm animals after implementation of BMPs. Dimensionless numbers and simple graphs are developed to assess how prevalence is influenced by a number of factors including animal density and farm spacing. A significant outcome of this model development is that the numerous dimensional input and parameter variables are reduced to a group of just four dimensionless Campylobacter-related quantities, characterizing: animal density; in-stream attenuation; animal-to-animal transmission; and infection recovery. Calculations reveal that for some constellations of these four quantities there can be a greater-than-expected benefit in that the proportional reduction of stream Campylobacter concentrations post-BMP can substantially exceed the proportional reduction of concentrations of E. coli in that stream. In addition, a criterion for system sterility (i.e., the conditions required for the farm infection rate to decrease with downstream distance) is derived.     

Drifting plastic and its consequences for sessile organism dispersal in the Atlantic Ocean

Organisms have travelled the Atlantic Ocean as neuston and have rafted on natural marine debris for millions of years. Shipping increased opportunities for marine organism travel mere thousands of years ago but in just decades floating plastic debris is transforming marine rafting. Here we present a combined open-ocean and remote coasts marine debris survey of the Atlantic (from 68°S–78°N). Daily shipboard observations were made from the Southern Ocean to the high Arctic and the shores of 16 remote islands were surveyed. We report (1) anthropogenic debris from the most northerly and southerly latitudes to date, (2) the first record of marine biota colonising debris at latitudes >68°, and (3) the finding of exotic species (the barnacle Elminius modestus) on northern plastic debris. Plastic pieces dominated both open-ocean and stranding marine debris. The highest densities of oceanic debris were found around northwest Europe, whereas the highest stranding levels were equatorial. Our findings of high east-Arctic debris colonisation by fauna contrast with low values from west Arctic (though only two samples) and south Atlantic shores. Colonisation rates of debris differed between hemispheres, previously considered to be similar. Our two South Atlantic mega-debris shipboard surveys (10 years apart) found no changes in open-ocean debris densities but resurvey of a UK and an Arctic island both found increases. We put our findings in the context of the Atlantic literature to interpret spatial and temporal trends in marine debris accumulation and its organismal consequences.Communicated by J.P. Thorpe, Port Erin     

Evaluation of some competition indices for the construction of Lebanon cedar (Cedrus libani A. Rich.) stand models

The purpose of this research is to test the precision of some published competition indices of Lebanon cedar (Cedrus libani A. Rich.) for the estimation of future periodic diameter increment of individual trees. Twenty- nine published competition indices were tested, using fifteen separate sets of data and their pooled values, collected from various stand age and site quality classes Lebanon cedar at Antalya. Temporary sample plots were taken in Elmali-Qamkuyusu (9 sample plots) and Finike-Pinarcik (6 sample plots) in 2001. Every plot was stem mapped (x and y coordinate system), diameter (dbh), total height, crown length, crown diameter and 10-year radial increment were recorded for trees greater than 4 cm in dbh. Then, in order to evaluate these competition indices for the prediction of the periodic diameter increment of the individual trees. Three linear models have been constructed for each competition index. It was found that the competition indices (Daniels et al., 1986; Biging and Dobbertin, 1995; Pukkala and Kolstr?m, 1987; Hegyi, 1974) with larger influence-zone areas produce better results.     

Contrasting effects of variable species recruitment on marine sessile communities

The species composition, density, and frequency of recruitment into any given habitat are highly variable in most biological systems that rely on dispersive propagules (larvae, seeds, spores, etc.). There are few direct experimental studies of how recruitment variation between single species influences the composition and assembly of whole communities in many of these systems. We manipulated recruitment of a variety of single taxa and followed their effects on the subsequent development of hard-substrate communities of sessile animals living in temperate marine waters. The effects of recruitment on communities were complex. Patterns of recruitment of individual species influenced community structure, but these effects varied greatly depending on the identity of species recruits, the time of community development, and location across three different sites. Variable recruitment of arborescent bryozoans and didemnid ascidians had little effect on community structure. At one site, recruitment of the colonial ascidian Botryllus schlosseri had short-lived effects on community structure, while barnacles had more persistent effects. At another site, recruitment of B. schlosseri and the bryozoan Watersipora subtorquata had strong persistent effects on community structure, dominating space where they recruited and influencing the abundances of a variety of different taxa. Differences in the effects of species recruitment on communities appear to be caused by differences between the ecology and life history of recruiting species as well as differences in background processes between sites. These results demonstrate that discrete recruitment events that vary between single species can be important drivers of community composition but are likely to be heavily influenced by the local environment, even within a single species.     

Genetic diversity increases population productivity in a sessile marine invertebrate

Reductions in genetic diversity can have widespread ecological consequences: populations with higher genetic diversity are more stable, productive and resistant to disturbance or disease than populations with lower genetic diversity. These ecological effects of genetic diversity differ from the more familiar evolutionary consequences of depleting genetic diversity, because ecological effects manifest within a single generation. If common, genetic diversity effects have the potential to change the way we view and manage populations, but our understanding of these effects is far from complete, and the role of genetic diversity in sexually reproducing animals remains unclear. Here, we examined the effects of genetic diversity in a sexually reproducing marine invertebrate in the field. We manipulated the genetic diversity of experimental populations and then measured individual survival, growth, and fecundity, as well as the size of offspring produced by individuals in high and low genetic diversity populations. Overall, we found greater genetic diversity increased performance across all metrics, and that complementarity effects drove the increased productivity of our high-diversity populations. Our results show that differences in genetic diversity among populations can have pervasive effects on population productivity within remarkably short periods of time.     

Persistence models for mark-recapture

The stable of models available for analyzing mark-recapture data (Otis et al. Wild Momogr 66:135, 1978) includes those having behavioral characteristics, time variation, heterogeneity, along with combinations of those characteristics. This paper proposes use of a series of models based on the persistence model of Ramsey and Usner (Biometrics 59:331–339, 2003). We show that persistence can be modeled in combination with behavior and with time variation. We apply the persistence model to situations in which capture occasions are not equally-spaced in time. Two case studies illustrate the use of these extended persistence models.     

Experimental evidence for mediation of competition by habitat succession

Habitat succession is thought to influence the importance of competition in assemblages. Competitive interactions are considered of critical importance in structuring ant assemblages, but field experiments show varied effects. I tested how succession in managed boreal forests affects the outcome of competition from dominant red wood ants, Formica aquilonia, through a removal experiment in replicated stands of three different ages (0-4, 30-40, and 80-100 years old). F. aquilonia abundance was reduced by 87%, and procedural controls showed no nontarget effects. The succession gradient revealed the full range of possible responses from ant species: decreases in 1-4-year-old stands, increases in 30-40-year-old stands, and no effects in 80-100-year-old stands, where diversity was lowest. Habitat succession thus regulates competitive interactions in this system. I propose a model for this system, where competitive effects depend on time since disturbance. In this case, soon after disturbance the dominant species facilitates increases in the abundance of other species. At intermediate times, competition reduces the abundance of some species. Finally, in long-undisturbed habitats, competitors may fail to evolve, particularly in high-stress environments. Interactions between competition and habitat succession may explain why structuring effects of ecologically dominant species appear inconsistent.     

Assessing the effectiveness of marine reserves on unsustainably harvested long-lived sessile invertebrates

Although the rapid recovery of fishes after establishment of a marine reserve is well known, much less is known about the response of long-lived, sessile, benthic organisms to establishment of such reserves. Since antiquity, Mediterranean red coral (Corallium rubrum) has been harvested intensively for use in jewelry, and its distribution is currently smaller than its historical size throughout the Mediterranean Sea. To assess whether establishment of marine reserves is associated with a change in the size and number of red coral colonies that historically were not harvested sustainably, we analyzed temporal changes in mean colony diameter and density from 1992 to 2005 within red coral populations at different study sites in the Medes Islands Marine Reserve (established in 1992) and in adjacent unprotected areas. Moreover, we compared colony size in the Medes Islands Marine Reserve, where recreational diving is allowed and poaching has been observed after reserve establishment, with colony size in three other marine protected areas (Banyuls, Carry-le-Rouet, and Scandola) with the enforced prohibition of fishing and diving. At the end of the study, the size of red coral colonies at all sampling sites in the Medes Islands was significantly smaller than predicted by growth models and smaller than those in marine protected areas without fishing and diving. The annual number of recreational dives and the percent change in the basal diameter of red coral colonies were negatively correlated, which suggests that abrasion by divers may increase the mortality rates of the largest red coral colonies within this reserve . Our study is the first quantitative assessment of a poaching event, which was detected during our monitoring in 2002, inside the marine reserve. Poaching was associated with a loss of approximately 60% of the biomass of red coral colonies.     

Shading facilitates sessile invertebrate dominance in the rocky subtidal Gulf of Maine

Dramatic shifts in community composition occur between vertical and horizontal rocky surfaces in subtidal environments worldwide, yet the forces mediating this transition are poorly understood. Vertical rock walls are often covered by lush, diverse communities of sessile suspension-feeding invertebrates, while adjacent horizontal substrates are dominated by algae, or corals in the tropics. Multiple factors, including light, sedimentation, water flow, and predation have been proposed to explain this pattern, but experimental tests of these hypotheses are lacking. We manipulated light level and predation to test whether variation in these mechanisms could be responsible for the shift in composition of sessile communities between vertical and horizontal surfaces in the rocky subtidal Gulf of Maine. Shaded horizontally oriented granite plots were dominated by invertebrates (e.g., ascidians, barnacles, bryozoans) after 25 months. Unshaded plots were dominated by macroalgae, which was virtually absent in shaded plots. Exclusion of grazers with cages had no effect on percent cover of invertebrates or algae. Preferential settlement of invertebrate larvae to shaded plots, due to larval behaviors such as negative phototaxis, did not seem to play a role. Shading likely affects post-settlement mortality of invertebrates by alleviating competition for space with algae, although greater abundance of micropredators in algal-dominated communities could also be important. Communities on shaded plots lacked many taxa present on natural wall communities, likely due to greater disturbance on horizontal substrates and/or lack of sufficient time for colonization of these taxa. These results suggest that light plays a key role in controlling the structure, composition, and function of shallow subtidal communities.     

Time-varying models for extreme values

We propose a new approach for modeling extreme values that are measured in time and space. First we assume that the observations follow a Generalized Extreme Value (GEV) distribution for which the location, scale or shape parameters define the space–time structure. The temporal component is defined through a Dynamic Linear Model (DLM) or state space representation that allows to estimate the trend or seasonality of the data in time. The spatial element is imposed through the evolution matrix of the DLM where we adopt a process convolution form. We show how to produce temporal and spatial estimates of our model via customized Markov Chain Monte Carlo (MCMC) simulation. We illustrate our methodology with extreme values of ozone levels produced daily in the metropolitan area of Mexico City and with rainfall extremes measured at the Caribbean coast of Venezuela.     

A reliability index for models

Since the prediction of environmental changes depends heavily on mathematical models, environmental planners have a definite need for a general test that can be easily applied to determine the reliability of a model or to choose between available models. In this paper a ‘reliability index’ for a model is defined. This index is a number k ? 1 which is determined from a set x₁,x₂,…,x_n of model predictions and a corresponding set y₁,y₂,…,y_n of observations. One interpretation of the index k is that the model predictions agree with observations, in some sense, within a factor of k. The index k is defined using an intuitive, geometric approach and is justified through agreement with another index developed using statistical techniques. Examples are given for a model which predicts the atmospheric movement of radon-222 originating from a concentrated source of radium-226, such as a uranium tailings pile.     

Persistence for ecosystem microcosm models

A qualitative analysis of a system of autonomous differential equations modelling an ecosystem microcosm is carried out from the point of view of persistence. Necessary and sufficient conditions are given that no trajectory with positive initial conditions has a component that tends to zero asymptotically or reaches zero in finite time. The results are stated in terms of threshold levels for the input nutrient parameter in the system.